Effect of ergodic and non-ergodic fluctuations on a charge diffusing in a stochastic Magnetic Field

TL;DR

This paper investigates how different types of magnetic field fluctuations, including ergodic and non-ergodic cases, influence the diffusion behavior of a charged particle, revealing conditions for normal and anomalous diffusion.

Contribution

It provides analytical and numerical analysis of particle diffusion under various stochastic magnetic field fluctuations, including non-Poissonian and diverging mean waiting times.

Findings

Field fluctuations cause both normal and anomalous diffusion.

Different fluctuation statistics lead to distinct diffusion regimes.

Results extend understanding beyond standard CTRW models.

Abstract

In this paper, we study the basic problem of a charged particle in a stochastic magnetic field. We consider dichotomous fluctuations of the magnetic field {where the sojourn time in one of the two states are distributed according to a given waiting time distribution either with Poisson or non-Poisson statistics, including as well the case of distributions with diverging mean time between changes of the field}, corresponding to an ergodicity breaking condition. We provide analytical and numerical results for all cases evaluating the average and the second moment of the position and velocity of the particle. We show that the field fluctuations induce diffusion of the charge with either normal or anomalous properties, depending on the statistics of the fluctuations, with distinct regimes from those observed, e.g., in standard Continuous Time Random Walk models.